Charged holostars

TL;DR

This paper introduces the charged holostar, an exact, singularity-free solution to Einstein's equations with a string-like interior, boundary membrane, and specific charge-energy properties, linking classical and quantum gravity concepts.

Contribution

It presents the charged holostar as a novel exact solution with unique interior structure, boundary conditions, and a connection to loop quantum gravity parameters.

Findings

The interior matter density is singularity-free and proportional to 1/r^2.

The holostar's geometric mass exceeds its charge, aligning with classical conditions for large objects.

The Immirzi parameter is derived and compared to LQG, showing a discrepancy explained in the paper.

Abstract

A charged holostar is an exact solution of the Einstein field equations. Its interior matter distribution rho = 1 / (8 pi r^2) is singularity free with an overall string equation of state. It has a boundary membrane of tangential pressure (but no mass-energy) situated roughly a Planck coordinate distance outside of the outer horizon of the RN-solution with the same mass and charge. The geometric mass Mg = M + r0/2 of a charged holostar is always larger than its charge. r0 is a Planck size correction to the gravitational mass M with r0 2 r_Pl. For a large holostar this condition is practically identical to the classical condition M >= Q. Whereas RN solutions with M < Q are possible, a charged holostar with Mg > Q doesn't exist. The total charge Q is derived by the proper integral over the interior charge density, which is attributed to the charged massive particles. The interior energy density splits into an electromagnetic and a "matter" contribution. Both contributions are proportional to 1/r^2. The ratio of electro-magnetic to total energy density rho_em / rho = 4 pi Q^2/A is constant throughout the whole interior. It is related to the dimensionless ratio of the exterior conserved quantities Q^2/A (or alternatively Q/M_g). An extremely charged holostar has a surface area A = 4 pi Q^2, so that its interior energy density consists entirely out of electromagnetic energy. A large holostar can be regarded as the classical analogue of a loop quantum gravity (LQG) spin-network state. The Immirzi parameter is determined: g = s /(pi \sqrt{3}), where s is the mean entropy per particle. g is larger by a factor of ~4.8 than the LQG-result. An explanation for the discrepancy is given.